Shape-Preserving and Convergence Properties for the q-Szász-Mirakjan Operators for Fixed q∈(0,1)
Joint Authors
Wang, Heping
Pu, Fagui
Wang, Kai
Source
Issue
Vol. 2014, Issue 2014 (31 Dec. 2014), pp.1-8, 8 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2014-05-06
Country of Publication
Egypt
No. of Pages
8
Main Subjects
Abstract EN
We introduce a q-generalization of Szász-Mirakjan operators Sn,q and discuss their properties for fixed q∈(0,1).
We show that the q-Szász-Mirakjan operators Sn,q have good shape-preserving properties.
For example, Sn,q are variation-diminishing, and preserve monotonicity, convexity, and concave modulus of continuity.
For fixed q∈(0,1), we prove that the sequence {Sn,qf} converges to B∞,q(f) uniformly on [0,1] for each f∈C[0, 1/(1-q)], where B∞,q is the limit q-Bernstein operator.
We obtain the estimates for the rate of convergence for {Sn,qf} by the modulus of continuity of f, and the estimates are sharp in the sense of order for Lipschitz continuous functions.
American Psychological Association (APA)
Wang, Heping& Pu, Fagui& Wang, Kai. 2014. Shape-Preserving and Convergence Properties for the q-Szász-Mirakjan Operators for Fixed q∈(0,1). Abstract and Applied Analysis،Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1033836
Modern Language Association (MLA)
Wang, Heping…[et al.]. Shape-Preserving and Convergence Properties for the q-Szász-Mirakjan Operators for Fixed q∈(0,1). Abstract and Applied Analysis No. 2014 (2014), pp.1-8.
https://search.emarefa.net/detail/BIM-1033836
American Medical Association (AMA)
Wang, Heping& Pu, Fagui& Wang, Kai. Shape-Preserving and Convergence Properties for the q-Szász-Mirakjan Operators for Fixed q∈(0,1). Abstract and Applied Analysis. 2014. Vol. 2014, no. 2014, pp.1-8.
https://search.emarefa.net/detail/BIM-1033836
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1033836